Question

question
solve the equation $x^2 - 19x + 2 = -2x^2$ to the nearest tenth.
answer attempt 1 out of 2
+ additional solution - no solution
$x = \square$ subn

Explanation:

Step1: Rearrange to standard quadratic form

$x^2 - 19x + 2 + 2x^2 = 0$
$3x^2 - 19x + 2 = 0$

Step2: Identify coefficients for quadratic formula

For $ax^2+bx+c=0$, $a=3$, $b=-19$, $c=2$

Step3: Apply quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:

$$ x=\frac{-(-19)\pm\sqrt{(-19)^2-4(3)(2)}}{2(3)} $$

Step4: Calculate discriminant

$\sqrt{361 - 24}=\sqrt{337}\approx18.3576$

Step5: Compute two solutions

First solution:
$x=\frac{19+18.3576}{6}=\frac{37.3576}{6}\approx6.2$
Second solution:
$x=\frac{19-18.3576}{6}=\frac{0.6424}{6}\approx0.1$

Answer:

$x\approx0.1$ and $x\approx6.2$